a) Does the the tape volume always run significantly lower than radio volume?
Not necessarily. (see Oldskool's response)
b) Also, has anyone noticed that self-made cassettes (often referred to as "mix tapes, though as a deejay, I hardly would call them that...) seem to carry more volume than store-bought cassettes?
YES. (see below)
I see what Eldo was generally trying to say, but I think his comments are way too general and don't do the subject full justice.
Ideally, when making a recording the goal is make it sound as indistinguishable from the source as possible. And to make really good recordings, you need good source material, good gear and good tapes.
Different tape types have different signal handling and background hiss characteristics. Normal tapes (type I) are typically the cheapest available and not really meant for critical mastering. They are good enough for recording from the radio, or copying a CD to play in a boombox. Now, with that said, there are actually some normal tapes out there that fall into what is often called the "super-ferric" category that can handle a tremendous amount of signal, somtemes even more than chrome (or type II) tapes. A few super ferric tapes that immediately come to mind are Maxell XL-IS, Fuji FR-ISuper & TDK AD-X. These haven't been made since the 90's and typically sell for hefty premiums on ebay.
Type II tapes (aka: high bias or chrome) tend to to be more expensive, but they also produce less background hiss and (for the most part) can handle more signal than the cheaper type I's. 90% of my 500 or so tapes are type II's.
Type IV tapes (Metal) have even better hiss characteristics than type II's and usually can take even more signal. However, many people feel the performance gain of using metal tapes over type II's do not justify the significantly increased cost. Here you are entering the realm of diminishing returns, where you pay a lot more for a seemingly minimal gain. I also believe that, for the most part a really good type II (like Maxell XL II, TDK SA or Fuji ZII) offers the best bang for the buck.
Features like Automatic Recording Level Control tend to be very conservative in recording volume to ensure the recording does not distort and typically do quieten down the signal a bit. Most component tape decks do not even have automatic level control, and the better boomboxes out there allow you to turn this feature off and manually adjust the recording level for a reason.
Typical prerecorded tapes are recorded onto cheap normal tape stock and peak at around 0db, which is a very conservative value and why you are probably asking these questions... As a result of the lower recording level it is easier to hear background hiss during quiet passages and between tracks, and why your radio seems alot louder than your tapes. I've actually gone so far as to cover the record tabs of some pre-recorded taps and record over them with the same material using a CD or record as the soucre in order to make the tape sound better. Most prerecorded tapes suck real bad when compared to what I can do when I record them myself.
Personally, I record my compilations or mixtapes (I'm a DJ, so when I say mixtape, its beatmixed
) to peak at anywhere from +3 to +6, depending on the quality of the cassette (not necessarily the type). I think most people who have experience making recordings do the same.
Also, I think its important to note that not all tapes within the above categories are equals. Brands and even the year of manufacture can make a huge difference as forumulations changed over the years. IMHO, the golden age of cassettes was between 1982 and 1990.
Sorry for the really long post, but audio tapes and recording are near and dear to my heart! I could go on with this topic forever! (and seemingly did). To learn more about various tape brands and tape recording in general you may want to check out
http://www.tapeheads.net as well.